Question

求极限lim(x→1) （³√x-1)/(√x-1)

求极限lim(x→1) （³√x-1)/(√x-1)

Answer 1

分子分母有理化就可以了
lim(x→1) （³√x-1)/(√x-1)
=lim(x→1) （³√x-1)（³√x^2+³√x+1)(√x+1)/[(√x-1)（³√x^2+³√x+1)(√x+1)]
=lim(x→1) (√x+1)/（³√x^2+³√x+1)
=2/3

Answer 2

求极限lim(x→1) （³√x-1)/(√x-1)
解：x→1lim（³√x-1)/(√x-1)
=x→1lim[（³√x-1)(³√x²+³√x+1)(√x+1)]/[(√x-1)(√x+1)(³√x²+³√x+1)]
=x→1lim[(x-1)(√x+1)]/[(x-1)³√x²+³√x+1)]=x→1lim(√x+1)]/(³√x²+³√x+1)=2/3

Answer 3

lim(x→1) （³√x-1)/(√x-1)
lim(x→1) (x^(1/3)-1)/(x^(1/2)-1)
= lim(x→1) (1/3x^(-2/3))/(1/2x^(-1/2))
=(1/3)/(1/2)=2/3

Answer 4

lim(x→1) （³√x-1)/(√x-1)
lim(x→1) (x^(1/3)-1)/(x^(1/2)-1)
= lim(x→1) (1/3x^(-2/3))/(1/2x^(-1/2))
=2/3